A CRJ700 FLT CREW RPTED THAT THEY COMPLIED WITH THE FIRST ZOB CTLR'S CLRNC WHO LATER HANDED THEM OFF TO THE NEXT ZOB CTLR WHO REVISED THEIR CLRNC FOR TFC SEPARATION.

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ORIGINALLY CRUISING AT FL370 DIRECT DKK; ZOB INSTRUCTED US TO TURN 20 DEGS L FOR TFC; DSND/MAINTAIN FL350. UPON LEVELING OR SHORTLY AFTER LEVELING AT FL350; ATC CLRED US TO FL330; BUT PRIOR TO REACHING FL330; CLRED US TO DSND TO FL290; TELLING US TO BRING IT DOWN WITH A GOOD RATE. BOTH PLTS HEARD EACH CLRNC AND PROPER ALT ALERTER PROTOCOL WAS FOLLOWED FOR EACH CHANGE TO THE ALT ALERTER. PRIOR TO REACHING FL290; THE CTLR THANKED US FOR THE DSCNT AND RECLRED US BACK DIRECT DKK; THEN GAVE US A FREQ CHANGE. ON CHK-IN; THE NEW CTLR ASKED US BOTH THE ALT WE WERE LEVELING AT AND OUR HDG. AFTER REPLYING THAT THE PREVIOUS CTLR CLRED US TO FL290 AND DIRECT DKK; WE WERE INSTRUCTED TO TURN L TO 330 DEGS FOR TFC 12 O'CLOCK POS; 5 MI; AND THEN GIVEN A DSCNT CLRNC TO FL250. WE MADE VISUAL CONTACT WITH THE OTHER TFC WHILE IN THE TURN; ALSO SAW ITS TCASII TARGET PASS JUST INSIDE THE 5 MI RING. NO TCASII TA OR RA SOUNDED DURING THE EVENT; AND AFTER CLR OF THE OTHER TFC; ATC RECLRED US DIRECT DKK. SUPPLEMENTAL INFO FROM ACN 620590: 119.72 SAID FL310 WAS OUR ALT ENTERED 'IN THE MACHINE?'